Asymptotic behaviors of forced waves for the lattice Lotka–Volterra competition system with shifting habitats

Recent developments on spatial propagation for diffusion equations in shifting environments

“…However, if the climate shifting speed is relatively large, there will exist a phase separation with expanding gap in which the densities of the retreated and invasive species decrease exponentially. Very recently, Qiao et al [83], Wang et al [95,96], Wang and Wu [98] extended and improved the result stated in Theorem 3.1 for (24) as well as its discrete and nonlocal dispersal versions. In particular, the authors of [95,96,98] showed that the invasion will be successful provided that the climate shifting speed falls into a certain interval containing the zero.…”

“…However, so far, there was little research in this respect for systems (24), ( 27) and (28). In particular, we have investigated the asymptotic behavior of forced wave for the lattice and nonlocal dispersal versions of competition system (24) with a special kind of growth functions in our recent paper [83,98]. The qualitative properties of forced waves for dispersal systems (24), ( 27) and (28), as an important research topic, is worthy of further discussion.…”

Speed determinacy of travelling waves for a three-component lattice Lotka–Volterra competition system

“…Traveling wave solutions play an important role in understanding the nonlinear biological and physical phenomena. Particularly, they usually can be applied to describe the spreading and invading behaviours in ecology [15,16,20,22,23,25]. The non-negative travelling wavefronts connecting e 1 to e 0 have the following form…”